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BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability

Samuel Daulton, David Eriksson, Maximilian Balandat, Eytan Bakshy

TL;DR

BONSAI addresses the usability gaps in Bayesian optimization by enforcing default-aware recommendations: starting from a candidate that maximizes the acquisition, it greedily reverts low-impact coordinates to a predefined default under a relative acquisition-gap constraint. The method is compatible with common acquisition functions (EI and GP-UCB) and provides a formal regret bound showing the cumulative loss from pruning is additive and controllable, preserving no-regret behavior under appropriate schedules. Empirically, BONSAI yields substantially sparser, more interpretable recommendations with comparable optimization performance and typically similar wall time, across synthetic and real-world problems including high-dimensional tasks. This makes BO more deployable in operational settings where changes from a vetted default incur risk or cost, without sacrificing efficiency or solution quality.

Abstract

Bayesian optimization (BO) is a popular technique for sample-efficient optimization of black-box functions. In many applications, the parameters being tuned come with a carefully engineered default configuration, and practitioners only want to deviate from this default when necessary. Standard BO, however, does not aim to minimize deviation from the default and, in practice, often pushes weakly relevant parameters to the boundary of the search space. This makes it difficult to distinguish between important and spurious changes and increases the burden of vetting recommendations when the optimization objective omits relevant operational considerations. We introduce BONSAI, a default-aware BO policy that prunes low-impact deviations from a default configuration while explicitly controlling the loss in acquisition value. BONSAI is compatible with a variety of acquisition functions, including expected improvement and upper confidence bound (GP-UCB). We theoretically bound the regret incurred by BONSAI, showing that, under certain conditions, it enjoys the same no-regret property as vanilla GP-UCB. Across many real-world applications, we empirically find that BONSAI substantially reduces the number of non-default parameters in recommended configurations while maintaining competitive optimization performance, with little effect on wall time.

BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability

TL;DR

BONSAI addresses the usability gaps in Bayesian optimization by enforcing default-aware recommendations: starting from a candidate that maximizes the acquisition, it greedily reverts low-impact coordinates to a predefined default under a relative acquisition-gap constraint. The method is compatible with common acquisition functions (EI and GP-UCB) and provides a formal regret bound showing the cumulative loss from pruning is additive and controllable, preserving no-regret behavior under appropriate schedules. Empirically, BONSAI yields substantially sparser, more interpretable recommendations with comparable optimization performance and typically similar wall time, across synthetic and real-world problems including high-dimensional tasks. This makes BO more deployable in operational settings where changes from a vetted default incur risk or cost, without sacrificing efficiency or solution quality.

Abstract

Bayesian optimization (BO) is a popular technique for sample-efficient optimization of black-box functions. In many applications, the parameters being tuned come with a carefully engineered default configuration, and practitioners only want to deviate from this default when necessary. Standard BO, however, does not aim to minimize deviation from the default and, in practice, often pushes weakly relevant parameters to the boundary of the search space. This makes it difficult to distinguish between important and spurious changes and increases the burden of vetting recommendations when the optimization objective omits relevant operational considerations. We introduce BONSAI, a default-aware BO policy that prunes low-impact deviations from a default configuration while explicitly controlling the loss in acquisition value. BONSAI is compatible with a variety of acquisition functions, including expected improvement and upper confidence bound (GP-UCB). We theoretically bound the regret incurred by BONSAI, showing that, under certain conditions, it enjoys the same no-regret property as vanilla GP-UCB. Across many real-world applications, we empirically find that BONSAI substantially reduces the number of non-default parameters in recommended configurations while maintaining competitive optimization performance, with little effect on wall time.
Paper Structure (48 sections, 8 theorems, 24 equations, 18 figures, 5 tables, 2 algorithms)

This paper contains 48 sections, 8 theorems, 24 equations, 18 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Background
  4. Bayesian optimization and GP surrogates.
  5. Acquisition functions.
  6. Related Work
  7. Conservative and safe bandits with baselines.
  8. Variable selection and shrinkage for high-dimensional BO.
  9. Explainable and interpretable BO.
  10. Sparse BO.
  11. BO with inexact acquisition maximization.
  12. Methodology
  13. Problem Setting
  14. Acquisition Gaps and Thresholded Pruning
  15. Sequential Greedy Pruning
  16. ...and 33 more sections

Key Result

Theorem 5.1

Assume the GP-UCB setting and kernel regularity conditions of srinivas and pmlr-v286-kim25b: in particular, $f\in\mathcal{H}_k$ with $\|f\|_{\mathcal{H}_k}\le B$, $k(x,x)\le 1$, and the noise is conditionally $R$-sub-Gaussian. Let $\alpha_t(\bm x) = \mu_{t-1}(\bm x) + \beta_t \sigma_{t-1}(\bm x)$ be

Figures (18)

  • Figure 1: This figure shows an example where parameters that have no effect end up at the boundary value. Starting with 5 training points (orange dots) from the function $f(\bm x) = (x_0 - 0.25)^2$, a GP correctly infers that only $x_0$ is relevant for modeling $f$. Even though the effect of $x_1$ is close to zero numerically (the GP lengthscale for $x_1$ is long), the maximizing EI yields a candidate at the boundary (purple square). BONSAI mitigates this issue by moving the $x_1$ back to its default value (green star).
  • Figure 2: Top row: Objective or HV. Bottom row: Best Objective (or HV) value for each level of active dimensions. For MOO, HV is plotted against the average number of active dimensions across points in the Pareto frontier.
  • Figure 3: Top row: objective or HV. Bottom row: Best Objective (or HV) value for each level of active dimensions. For MOO, HV is plotted against the average number of active dimensions across points in the Pareto frontier.
  • Figure 4: Real-world Ranking Problems. Top row: Objective or HV. Bottom row: Best Objective (or HV) value for each level of active dimensions. For MOO, HV is plotted against the average number of active dimensions across points in the Pareto frontier.
  • Figure 5: Optimization performance of BONSAI with batch optimization ($q=5$) on synthetic problems. Top row: Objective or HV. Bottom row: Best Objective (or HV) value for each level of active dimensions. For MOO, HV is plotted against the average number of active dimensions across points in the Pareto frontier.
  • ...and 13 more figures

Theorems & Definitions (14)

  • Theorem 5.1: Regret bound via accumulated inaccuracy
  • Corollary 5.1: Asymptotic No-Regret
  • Lemma 1.0: Relative rule implies accuracy lower bound
  • proof
  • Theorem 1.1: Regret bound via accumulated inaccuracy
  • proof
  • Corollary 1.0: Asymptotic No-Regret
  • proof
  • Corollary 1.0: Example schedules
  • proof
  • ...and 4 more